P3D Re: Curious Deep Math Tale

[aifxtony@xxxxxxxxxxxxx (Tony Alderson)]

>Dr. George A. Themelis (digest 2891) wrote:
>Michael Georgoff noticed something curious:

>>It appears that stereo base is dependent on f-stop. That is all. Stereo
>>base in mm = 1200/f-stop.

>You have just discovered that the formulas for the Depth of Field and the
>Stereoscopic Deviation are very similar....(deleted)....<

This is a very interesting point, but let's not take it too far. Stereo
base is not solely dependent on f-stop.

It is helpful to know that on an ASA stereo camera (e.g., the Realist,
etc.) the projectable depth range is the same as the distance between the
f5.6 marks on the DOF scale. However, keep in mind that if you actually
expose at f11, (which may be necessary with today's faster films and the
Realist's slow shutter), your depth range does not increase to the f11
marks!

Consider this experiment:

You will need an SLR, a slide bar, lenses of two focal lengths. (for now,
I'll assume a 40mm lens and a 75mm lens) We will assume the lenses are
calibrated in T-stops, so we can ignore the transmission differences of the
glass. We will assume some appropriate reference scene.

If we take two stereo pairs with the 40mm lens with a 50mm interaxial, one
pair at f5.6, and the other at f22 (adjusting the shutter to compensate the
exposure); then take two equivalent stereo pairs, only with the 75mm lens;
we will find:

1.  The stereos taken with the same focal length lens will have identical
on film parallax, regardless of f-stop.

2.  The stereos taken with the 40mm lens will show less parallax for the
same distance than the 75mm stereos, regardless of f-stop.

I don't doubt Dr. T understands this...as he slyly closes:

>Hope this helps (or puts you in the right track)<

This sounds like some kind of teacher's trick to make one think.

I don't think it's necessary to work through the whole depth-range equation
every time one takes a stereo, but P3D'ers may find it educational to work
through a few examples. I found it helped me understand the relationships
so I could make better informal estimates. Look to Piper, or Lipton, or
Spottiswode, or Ferwerda for the formula; they all use the same thing,
although it may be in different forms or use different letters for the
variables. And you'll finally have found a practical use for all that
algebra and trig you took in high school (parents take note!).

Tony Alderson
aifxtony@xxxxxxxxxxxxx




------------------------------